 96573 Anton Bovier, Veronique Gayrard
 AN ALMOST SURE CENTRAL LIMIT THEOREM FOR THE HOPFIELD MODEL
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Nov 18, 96

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Abstract. We prove a central limit theorem
for the finite dimensional marginals of the Gibbs distribution
of the macroscopic `overlap'parameters in the Hopfield model
in the case where the number of random `patterns', $M$, as a
function of the system size $N$ satisfies
$\lim_{N\uparrow\infty} M(N)/N=0$, without any
assumptions on the speed of convergence.
The covariance matrix of the limiting gaussian distributions is
diagonal and independent of the disorder for almost
all realizations of the patterns.
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